I've been running Remote Desktop through a VPN from the laptop in the Norfolk hideaway back to the PC in the Essex house for years, and it "just works".
I can also access the Linux machine in Essex, using VNC Server.
The hard drives on both Essex machines are shared, and I can access files on them without using Remote Desktop. Everything was very easy to set up, and works perfectly.
My ISP provides a static IP address, so no worries about that. Otherwise, I think dyndns is the one most folks use.